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ABSTRACT
Almost by definition, well-tuned digital circuits have a large number of equally critical paths, which form a so-called "wall" in the slack histogram. However, by the time the design has been through manufacturing, many uncertainties cause these carefully aligned delays to spread out. Inaccuracies in parasitic predictions, clock slew, model-to-hardware correlation, static timing assumptions and manufacturing variations all cause the performance to vary from prediction. Simple statistical principles tell us that the variation of the limiting slack is larger when the height of the wall is greater.Although the wall may be the optimum solution if the static timing predictions were perfect, in the presence of uncertainty in timing and manufacturing, it may no longer be the best choice. The application of formal mathematical optimization in transistor sizing increases the height of the wall, thus exacerbating the problem. There is also a practical matter that schematic restructuring downstream in the design methodology is easier to conceive when there are fewer equally critical paths. This paper describes a method that gives formal mathematical optimizers the incentive to avoid the wall of equally critical paths, while giving up as little as possible in nominal performance. Surprisingly, such a formulation reduces the degeneracy of the optimization problem and can render the optimizer more effective. This "uncertainty-aware" mode has been implemented and applied to several high-performance microprocessor macros. Numerical results are included.
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Aseem Agarwal , David Blaauw , Vladimir Zolotov , Sarma Vrudhula, Computation and Refinement of Statistical Bounds on Circuit Delay, Proceedings of the 40th conference on Design automation, June 02-06, 2003, Anaheim, CA, USA
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Matthew R. Guthaus , Natesan Venkateswaran , Vladimir Zolotov , Dennis Sylvester , Richard B. Brown, Optimization objectives and models of variation for statistical gate sizing, Proceedings of the 15th ACM Great Lakes symposium on VLSI, April 17-19, 2005, Chicago, Illinois, USA
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Ashish Srivastava , Saumil Shah , Kanak Agarwal , Dennis Sylvester , David Blaauw , Stephen Director, Accurate and efficient gate-level parametric yield estimation considering correlated variations in leakage power and performance, Proceedings of the 42nd annual conference on Design automation, June 13-17, 2005, San Diego, California, USA
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Aseem Agarwal , Kaviraj Chopra , David Blaauw , Vladimir Zolotov, Circuit optimization using statistical static timing analysis, Proceedings of the 42nd annual conference on Design automation, June 13-17, 2005, San Diego, California, USA
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Jaskirat Singh , Vidyasagar Nookala , Zhi-Quan Luo , Sachin Sapatnekar, Robust gate sizing by geometric programming, Proceedings of the 42nd annual conference on Design automation, June 13-17, 2005, San Diego, California, USA
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Animesh Datta , Swarup Bhunia , Jung Hwan Choi , Saibal Mukhopadhyay , Kaushik Roy, Speed binning aware design methodology to improve profit under parameter variations, Proceedings of the 2006 conference on Asia South Pacific design automation, January 24-27, 2006, Yokohama, Japan
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N. Ranganathan , U. Gupta , V. Mahalingam, Simultaneous optimization of total power, crosstalk noise, and delay under uncertainty, Proceedings of the 18th ACM Great Lakes symposium on VLSI, May 04-06, 2008, Orlando, Florida, USA
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Xin Li , Jiayong Le , Mustafa Celik , L. T. Pileggi, Defining statistical sensitivity for timing optimization of logic circuits with large-scale process and environmental variations, Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design, p.844-851, November 06-10, 2005, San Jose, CA
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K. Chopra , S. Shah , A. Srivastava , D. Blaauw , D. Sylvester, Parametric yield maximization using gate sizing based on efficient statistical power and delay gradient computation, Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design, p.1023-1028, November 06-10, 2005, San Jose, CA
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M. R. Guthaus , N. Venkateswarant , C. Visweswariaht , V. Zolotov, Gate sizing using incremental parameterized statistical timing analysis, Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design, p.1029-1036, November 06-10, 2005, San Jose, CA
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